Chapter

Object and Truth

Stewart Shapiro

in Philosophy of Mathematics

Published in print October 2000 | ISBN: 9780195139303
Published online November 2003 | e-ISBN: 9780199833658 | DOI: http://dx.doi.org/10.1093/0195139305.003.0003
 Object and Truth

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Several varieties of realism are distinguished. Working realism is a methodological thesis that sanctions the inferences and principles suggested by traditional realism: excluded middle, the axiom of choice, impredicative definition, and general extensionality. Working realism is consistent with antirealist philosophical positions. Realism in ontology, sometimes called “platonism”, is the philosophical view that mathematical objects exist independent of the mind, language, or form of life of the mathematician. Realism in truth value is the view that mathematical assertions have objective truth values independent of the mind, language, or form of life of the mathematician. The relations between these realism are articulated, and the results are related to Quine's ontological, epistemological, and semantic themes.

Keywords: antirealism; axiom of choice; excluded middle; extensionality; impredicative definition; object; objectivity; ontology; Platonism; Quine; realism; truth value

Chapter.  17671 words. 

Subjects: Philosophy of Mathematics and Logic

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